Extending gaussian hypergeometric series to the p-adic setting

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Abstract

We define a function which extends Gaussian hypergeometric series to the p-adic setting. This new function allows results involving Gaussian hypergeometric series to be extended to a wider class of primes. We demonstrate this by providing various congruences between the function and truncated classical hypergeometric series. These congruences provide a framework for proving the supercongruence conjectures of Rodriguez-Villegas.

Original languageEnglish
Pages (from-to)1581-1612
Number of pages32
JournalInternational Journal of Number Theory
Volume8
Issue number7
DOIs
StatePublished - Nov 2012

Keywords

  • Gaussian hypergeometric series
  • generalized hypergeometric series
  • hypergeometric functions over finite fields
  • p-adic gamma function
  • supercongruence

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